Relatives of the 96 victims of the Hillsborough disaster have said they feel vindicated in their 23-year campaign for justice after the original inquest verdict of accidental death was quashed in the high court.

The landmark verdict clears the way for a new inquest into the deaths next year, re-examining the roles of the police and other emergency services, Sheffield council and Sheffield Wednesday Football Club, and leading to the possibility of new verdicts of unlawful killing.

The lord chief justice said it was "inevitable" that the emergence of fresh evidence about how and why the 96 victims died made it "desirable and reasonable for a fresh inquest to be heard".

"However distressing or unpalatable, the truth will be brought to light," Lord Judge said. "In this way, the families of those who died in the disaster will be properly respected. Our earnest wish is the new inquest will not be delayed for a moment longer than necessary."

The decision came as a new police investigation into the disaster was announced by the home secretary, Theresa May. The former Durham chief constable Jon Stoddart will lead the new inquiry and liaise with a parallel Independent Police Complaints Commission review.

The application by the attorney general, Dominic Grieve, to quash the original verdicts was made in the wake of the publication in September of the Hillsborough Independent Panel (HIP) report and accepted by three high court judges.

New medical evidence revealed that 58 victims "definitely or probably" had the capacity to survive beyond the 3.15pm cut-off point imposed by the original coroner, Dr Stefan Popper. In a further 12 cases, the cause of death remained unclear.

Grieve said the application was unopposed and supported by all the families and the defendants, the coroner for South Yorkshire and the coroner for West Yorkshire.

The original coroner said that no evidence gathered after 3.15pm, when the first ambulance arrived on the pitch, would be considered because he believed that by that point all 96 victims were already dead. As a result, the role of the police and the emergency services in the aftermath of the disaster was not considered.

The attorney general told the court that medical evidence from Dr Bill Kirkup and Prof Jack Crane formed "the essential basis" for his application, meaning that the premise of the original inquest was unsustainable.

"The new medical evidence presented by the panel's report leads to the conclusion that justice has not been done," he said.

The lord chief justice said there was "ample evidence to suggest that the 3.15pm cut-off was seriously flawed" and that was sufficient on its own to justify the quashing of the original inquest.

It raised new questions about the conduct of police and the emergency services, he said.

But he said there were other reasons for ordering a new inquest, including the 116 amendments to police statements designed to cast them in a better light, and new evidence about the safety of the stadium.

Set up to reconsider all evidence relating to the disaster, including new documents made available for the first time, the HIP report raised serious concerns about the adequacy of the original inquest in Sheffield in 1990.

The review found that the decision to impose the cut-off severely limited examination of the response of the police and emergency services to the disaster on 15 April 1989, in which 96 Liverpool fans were crushed to death in the Leppings Lane end of the stadium, and "raised profound concerns regarding sufficiency of inquiry and examination of evidence".

The lord chief justice agreed, saying that "in our judgment the 3.15pm cut-off point provided not only the most dramatic but also the most distressing aspect" of the new evidence.

"In short, the unchallenged evidence of pathologists at the Taylor inquiry and the subsequent inquest is no longer accepted," he said.

The original verdict of accidental death, delivered by a jury in March 1991 following the longest inquest in British legal history, has been a running sore for the families of those killed in the disaster, who felt the inquest was wholly inadequate.

Many of the relatives of those killed were present on Wednesday in court five of the Royal Courts of Justice on the Strand or watching via videolink in an adjacent courtroom. Some held pictures of their relatives and others carried Liverpool scarves.

Trevor Hicks, chair of the Hillsborough Family Support Group, said afterwards: "Justice is on its way. Everything we've said has been proven to be correct."

Some of the MPs who campaigned for a new investigation of the full facts surrounding the disaster, including Andy Burnham and Steve Rotheram, watched from the public gallery. In Liverpool, another 150 relatives watched via videolink at the civil and family courts.

"I was very pleased that he opened up the whole question of the years preceding Hillsborough and ground safety," said Burnham.

"That seems to me to be absolutely the key question of the new inquest. Should this have been prevented? We've always argued it should. Was it an accident? We've always argued it was not. He's set that up now. I'm overwhelmed with the strength of his ruling."

Rotheram said families who lost relatives in the Hillsborough disaster have said the state should meet the cost of any new inquest.

"This verdict marks the beginning of the end of the Hillsborough disaster. At long last the families have achieved their ultimate goal which is to change the verdict on the death certificates," he said.